They have agreed to cut debts by 40bn euros ($51bn; £32bn) and have paved the way for releasing the next tranche of bailout loans – some 44bn euros.
Greek Prime Minister Antonis Samaras welcomed the deal, saying “a new day begins for all Greeks”.
Asian shares climbed on news of the agreement.
MSCI’s broadest index of Asia Pacific shares outside Japan gained 0.6% to its highest in more than two weeks.
Australian shares rose 0.7%, while South Korea’s benchmark Kospi index was up nearly 1%.
The euro reached its highest level against the dollar since 31 October, up about 0.3% to $1.3010.
The breakthrough came after more than 10 hours of talks in Brussels. It was the eurozone’s third meeting in two weeks on Greece.
The deal opens the way for support for Greece’s teetering banks and will allow the government to pay wages and pensions in December.
We simply could not afford to fail”
Olli Rehn EU economic and monetary affairs comissioner
The leader of the eurozone finance ministers’ group, Jean-Claude Juncker, said Greece would get the next installment of cash on 13 December.
Greece has been waiting since June for the tranche, to help its heavily indebted economy stay afloat.
European Central Bank (ECB) president Mario Draghi said the bailout would “strengthen confidence in Europe and in Greece”.
For his part, Mr Juncker said the deal did not just have financial implications.
“This is not just about money. It is the promise of a better future for the Greek people and for the Euro area as a whole.”
Greece’s international lenders have agreed to take steps to reduce the country’s debts, from an estimated 144%, to 124% of its gross domestic product by 2020.
These include cutting the interest rate on loans to Greece, and returning 11bn euros to Athens in profits from ECB purchases of Greek government bonds.
Ministers have also agreed to help Greece buy back its own bonds from private investors.
So far the ECB, IMF and the European Commission have pledged a total of 240bn euros in rescue loans, of which Greece has received around 150bn euros.
In return, Greece has had to impose several rounds of austerity measures and submit its economy to scrutiny.
The European Union’s commissioner for economic and monetary affairs, Olli Rehn, said it was crucial that a deal had finally been reached.
“For the eurozone this was a real test of our credibility, of our ability to take decisions on the most challenging of issues.
“And it was a test that we simply could not afford to fail.”